Theoretical analysis and numerical simulation of a weak periodic solution for a parabolic problem with nonlinear boundary conditions

Abdelwahab Elaassri, Kaoutar Lamrini Uahabi, Malika El Ghabi, Abderrahim Charkaoui, Nour Eddine Alaa

Abstract


The aim of this work is to develop a numerical tool for computing the weak periodic solution for a class of parabolic equations with nonlinear boundary conditions. We formulate our problem as a minimization problem by introducing a least-squares cost function. With the help of the Lagrangian method, we calculate the gradient of the cost function. We build an iterative algorithm to simulate numerically the weak periodic solution to the considered problem. To illustrate our approach, we present some numerical examples.

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DOI: https://doi.org/10.52846/ami.v51i1.1740